From The Thomas Nelson Open Bible Study Notes:
The casting of lots was a custom or rite used in ancient times to make important decisions, much as we practice drawing straws or flipping a coin today. Several examples of this practice occur in both the Old and New Testaments.
Lots were cast by the high priest to select the scapegoat on the Day of Atonement. (Lev 16:8-10). This method was also used to divide the land of Canaan after its conquest under Joshua (Num. 26:55,56; Josh. 14:2). Lots were cast to select warriors to fight against the men of Gibeah (Judg. 20:9,10) and apparently to choose Saul as the first king of Israel (1 Sam. 10:19-21). Sailors on the ship bound for Tarshish with Jonah on board used lots to determine who had caused the stormy seas (Jon 1:7).
In the New Testament, Roman soldiers cast lots for Jesus' garments (Matt. 27:35). After prayer, the apostles used lots to choose Matthias as successor to Judas (Acts 1: 24-26).
We can only speculate about what materials were used in the casting of lots. Some scholars believe several stones, or perhaps precious gems, were cast from a clay jug. Others connect the practice with Urim and Thummin, precious stones that were on, by or in the breastplate of the high priest of Israel. The high priest used these stones in making important decision, but it is not known exactly how this was done (Ex. 28:30).
"The lot is cast into the lap; but the whole disposing thereof is of the LORD."
Proverbs 16:33 demonstrates above that casting lots was not considered magic, because the decision was from the Lord.
I'm not sure how good the source is on this. I'll look for more.
The transliteration of the Greek is "Lagcano" and means to obtain by lot or by divine allotment. The word appears elsewhere in the NT in 2 Peter 1:1
"Simon Peter, a servant and an apostle of Jesus Christ, to them that have obtained like precious faith with us through the righteousness of God and our Saviour Jesus Christ:
and John 19:24
They said therefore among themselves, Let us not rend it, but cast lots for it, whose it shall be: that the scripture might be fulfilled, which saith, They parted my raiment among them, and for my vesture they did cast lots. These things therefore the soldiers did.
There is no mention anywhere that I've found of the word ever indicating any kind of voting or balloting.
Chapter 1 > Verse 26 John Gill's Exposition of the Bible
Acts 1:26
And they gave forth their lots… Or "gave forth lots for them", as the Vulgate Latin and Ethiopic versions; for Joseph and Matthias; some for one, and some for another; and which were cast into a man's lap, or into a vessel, and was no other than balloting for them; and so he that had the majority upon casting them up, when taken out, was declared the person chosen; or "they cast their lots"; that is, into an urn, or vessel; which lots had the names of the two persons on them; and into another vessel, as is thought, were put two other lots; the one had the name of "apostle" upon it, and the other nothing; and these being taken out by persons appointed for that purpose, the lot with Matthias's name on it, was taken out against that which had the name of apostle on it, upon which he was declared to be the apostle: it may be that this was done in the same manner, as the goats on the day of atonement had lots cast on them, (Leviticus 16:8) which the Jews say was thus performed: there was a vessel which they call "Kalphi", set in the court, into which two lots, which were made of wood, or stone, or metal, were put; the one had written on it, for Jehovah, and on the other was written, "for the scapegoat"; the two goats being, the one at the right hand of the priest, and the other at the left; the priest shook the vessel, and with his two hands took out the two lots, and laid the lots on the two goats; the right on that which was at his right hand, and the left on that which was at his left F9; and so the goat which had the lot put upon him, on which was written, "for the Lord", was killed; and that which had the other lot, on which was written, for the scapegoat, was presented alive; so the lot here is said to fall upon Matthias: or the lots being cast into the vessel, as above related, these two drew them out themselves; and Matthias taking out that which had the word apostle on it, the lot fell on him: the manner of Moses's choosing the seventy elders, is said to be this F11:
etc.............